Booth algorithm (multiplication of signed numbers)

Ask for M3m2m1m0xq3q2q1q0:0110x0101 (signed number is in complement, the highest bit is positive or negative)

1. Add auxiliary bit: a=0000 q-1=0

2. Control logic judgment:

①Q0Q-1=01: A=a+m then A, Q, Q-1 arithmetic right shift (two steps)

②q0q-1=10: A=a-m then A, Q, Q-1 arithmetic right shift (two steps)

Complement plus minus: (A-M) complement =a complement + (-m) complement

③q0q-1=00 or 11 o'clock: A, Q, Q-1 arithmetic right shift (one step)

Complement right shift: empty 1

3, q A few do several right-shift operations. (eg: 01000x011, do 3 right Shift end)

4, the result is AQ (0001 1110, that is, 6x5=30).

operation process and results

	A	Q	Q-1	M
Initial	0000	0101	0	0110
①a-m	1010	0101	0	0110
A,q,q-1 Right Shift	1101	0010	1	0110
②a+m	0011	0010	1	0110
A,q,q-1 Right Shift	0001	1001	0	0110
③a-m	1011	1001	0	0110
A,q,q-1 Right Shift	1101	1100	1	0110
④a+m	0011	1100	1	0110
A,q,q-1 Right Shift	0001	1110	0	0110

Booth algorithm (multiplication of signed numbers)